Boundedness of Operators and Inequalities on Morrey-Banach Spaces

This paper establishes the boundedness of the spherical maximal function, Rubio de Francia operators, Bochner-Riesz operators, Fourier integral operators, geometric maximal operator, minimal operator and strongly singular integral operators on Morrey spaces built on Banach function spaces. We also establish the Coifman-Fefferman inequalities, Gundy-Wheeden inequalities and Sobolev-Lieb-Thirring inequalities on Morrey-Banach spaces. In particular, our results include the boundedness of the above operators and inequalities on classical Morrey spaces, generalized Morrey spaces, Orlicz-Morrey spaces, Morrey-Lorentz spaces and Morrey spaces with variable exponents.